The present invention relates to a method of generating a pulse train of laser pulses, in particular by mode-coupling of resonator modes of a laser resonator. Furthermore, the invention relates to a spectroscopy method for investigating a sample, using the pulse train of laser pulses. Furthermore, the invention relates to a laser pulse source apparatus and a spectroscopy apparatus including the laser pulse source apparatus. Applications of the invention are available e.g. in laser physics, in particular spectroscopy.
In the present specification, reference is made to the following prior art illustrating the technical background of the invention:    [1] Th. Udem et al. in “Nature” 416, 233 (2002);    [2] M. Hofer et al. in “Opt. Lett.” 16, 502 (1991);    [3] T. Ideguchi et al. in “Nat. Commun.” 5, 3375 (2014);    [4] B. Bernhardt et al. in “Nature photonics” 4, 55 (2010);    [5] S. Teng et al. in “Opt. Commun.” 315, 103 (2014);    [6] J. Azaña et al. in “Appl. Opt.” 38, 6700 (1999);    [7] T. Suzuki et al. in “Opt. Expr.” 18, 23088 (2010).
Creating laser pulses by mode-coupling of resonator modes of a laser resonator is generally known. Conventional pulse lasers typically create a pulse train of laser pulses, which can be represented in frequency space as a frequency comb with equidistant comb modes, resulting from the temporal periodicity of the pulse train (e.g. [1]).
Pulse lasers creating frequency combs, like e.g. mode-locked fiber lasers [2] have numerous applications in laser physics, metrology, spectroscopy and/or attosecond pulse generation. In particular, dual-comb spectroscopy has been proposed [3, 4], wherein Fourier transform spectroscopy is conducted with two conventional frequency combs each having an equidistant mode spacing. A first frequency comb is transmitted through a sample and afterwards superimposed with a second frequency comb having a slightly different repetition rate compared with the first frequency comb. The first and second frequency combs interfere, so that beating signals in the radio frequency range are obtained, which can be measured with a photo diode, resulting in information on the interaction of the mode frequencies of the first frequency comb with the sample. Conventional dual-comb spectroscopy has disadvantages in terms of the required two separate frequency combs, the necessary stabilization thereof and the need for a so-called adaptive sampling of the photo diode signal. In particular, the application of the dual-comb spectroscopy is limited by a relative jitter of the combs.
The Talbot effect has been described for the first time in 1836 as a peculiar phenomenon observed in the near field of an optical grating. Summing over contributions of the individual rulings to the total field in the Fresnel approximation, a term of the form
  exp  (      -                            ikl          2                ⁢                  a          2                            2        ⁢        z              )appears with the wave number k, the rulings numbered by l and spaced by a and the distance from the grating z. Summing over l generally yields a rather complex intensity distribution. Talbot noted though that this term reduces to exp(−i2πl2)=1 at a distance of z=ka2/4π. The remaining terms add up to the intensity at z=0 provided that this intensity is periodic with a [5].
The same phenomenon can be observed in the time domain with a periodic pulse train signal that is subject to group velocity dispersion k″ (where k″ is the second derivative of k (ω) vs frequency ω) that provides the quadratic phase evolution (temporal Talbot effect). The pulses first spread out in time, and then reassemble after propagation the distance tr2/(2π|k″|), where tr is the pulse repetition time [6, 7]. In the past, the temporal Talbot effect has been used for pulse compression outside the laser resonator only.